It is: 4023/6 = 670 with a remainder of 3
2x2-4x+5 divided by x-1 Quotient: 2x-2 Remainder: 3
To find the remainder when dividing ( x^3 + 2x + 13 ) by ( x^3 ), we can use the polynomial remainder theorem. Since the degree of the divisor ( x^3 ) is equal to the degree of the dividend ( x^3 + 2x + 13 ), the remainder will be a polynomial of lower degree than ( x^3 ). Therefore, the remainder is simply the result of the division, which is ( 2x + 13 ).
When a polynomial ( P(x) ) is divided by ( (x + a) ), the remainder can be found using the Remainder Theorem. This theorem states that the remainder of the division of ( P(x) ) by ( (x - r) ) is equal to ( P(r) ). Therefore, when dividing by ( (x + a) ), which is equivalent to ( (x - (-a)) ), the remainder is ( P(-a) ), confirming that ( P(-a) ) is the value of the polynomial evaluated at ( -a ).
Add seven to any multiple of 8. 63 divided by 8 has a remainder of 7.
The answer would be 100, with 34 remainder.
True.
2x2-4x+5 divided by x-1 Quotient: 2x-2 Remainder: 3
To find the remainder when dividing ( x^3 + 2x + 13 ) by ( x^3 ), we can use the polynomial remainder theorem. Since the degree of the divisor ( x^3 ) is equal to the degree of the dividend ( x^3 + 2x + 13 ), the remainder will be a polynomial of lower degree than ( x^3 ). Therefore, the remainder is simply the result of the division, which is ( 2x + 13 ).
7.8
True-APEX
When 50 is divided by 8, the quotient is 6 with a remainder of 2. This means that 50 can be expressed as 8 times 6 plus 2. The remainder of 2 is what remains after dividing 50 by 8.
4.8571
ccc plus exam result 2009
When a polynomial ( P(x) ) is divided by ( (x + a) ), the remainder can be found using the Remainder Theorem. This theorem states that the remainder of the division of ( P(x) ) by ( (x - r) ) is equal to ( P(r) ). Therefore, when dividing by ( (x + a) ), which is equivalent to ( (x - (-a)) ), the remainder is ( P(-a) ), confirming that ( P(-a) ) is the value of the polynomial evaluated at ( -a ).
2,019,045
c2 - 4 = (c+2)*(c-2) So, dividing by (c+2) leaves the other factor: (c-2)
(x^3 + 3x^2 - x - 2)/[(x + 3)(x + 5) in this case you can use the long division to divide polynomials and to find the remainder of this division. But you cannot use neither the synthetic division to divide polynomials nor the Remainder theorem to determine the remainder. You can use both the synthetic division and the Remainder theorem only if the divisor is in the form x - c. In this case the remainder must be a constant because its degree is less than 1, the degree of x - c. The remainder theorem says that if a polynomial f(x) is divided by x - c, then the remainder is f(c). If the question is to determine the remainder by using the remainder theorem, then you are asking to find the value of f(-3) when you are dividing by x + 3, or f(-5)when you are dividing by x + 5 . Just substitute -3 or -5 with x into the dividend x^3 + 3x^2 - x - 2, and you can find directly the value of the remainder. f(-3) = (-3)^3 + 3(-3)^2 - (-3) - 2 = -27 + 27 + 3 - 2 = 1 (remainder is 1) f(-5) = (-5)^3 + 3(-5)^2 - (-5) - 2 = -125 + 75 + 5 - 2 = -47 (remainder is -47).